How to break Magic the Gathering.

[00:00] Are you ready for the biggest number I believe 

[00:05] generated, I think is like super interesting. 

[00:11] the Gathering, which is why I have all these 

[00:15] friends of mine do, who are massive dorks, and 

[00:20] now. They assure me it's a lot of fun, and I get 

[00:25] which is how we get this ridiculous number. 

[00:30] got a worm spelled incorrectly. And then you 

[00:35] the game because it's like a two-player 

[00:38] soot. Don't know what that is. Uh and Armageddon, 

[00:51] I regret calling them dorks.

[01:00] This video brought to you by Jane Street and their 

[01:08] we're going to need somewhere new to film. 

[01:13] the Gathering is it's been around for now over a 

[01:18] not right, Matt, it came out in 1993. I have some 

[01:26] it started well it was the brainchild of someone 

[01:32] complicated since and over the three decades 

[01:38] up. There are now almost 30,000 different cards. 

[01:46] unwieldy level of complex. And for that reason, 

[01:53] from getting too out of hand. Because a lot of the 

[01:58] 107.1 states that only whole numbers are allowed, 

[02:08] simple. If it's something you can't calculate 

[02:14] tough. If you can't calculate it, you get a zero. 

[02:21] of cars interacting, you think, well, hang on. 

[02:26] Well, regulation 104.4B says no to that. If you've 

[02:35] is going to carry on infinitely long, no deal. 

[02:43] it's a cycle where no player can stop it. If a 

[02:47] choose some some arbitrary level at which at which 

[02:54] you can only play moves which will give you a 

[03:00] was nice and manageable for a very long time 

[03:06] big numbers, but before infinity. Our ridiculous 

[03:14] have managed to get our hands on the original. 

[03:21] h they are dense. There's a lot of like wonderful 

[03:26] And so what we've done is we've made three 

[03:32] going to use those to explain how it all works. 

[03:41] this card doubles the number of tokens that are 

[03:46] have like your original creature cards or like you 

[03:52] them that are called tokens. And the game deals 

[03:57] all the token copies. This is if you're putting in 

[04:02] we'll get to card B in a moment because before 

[04:07] card C says once you do play B, you're going to 

[04:13] you've got A and C ready, our ridiculous loop is 

[04:20] in the original is called Astral Dragon. We've 

[04:27] you make two token copies of A. So, in theory, 

[04:34] But because they're tokens entering the game, 

[04:39] double them. So, we'd actually get four. So, 

[04:44] four token copies of A appearing as if by magic, 

[04:53] okay, this card over here, I know I'm going 

[04:58] card says I can search search your library. So, 

[05:12] So, at my local library, I was able to make some 

[05:19] them apart, gives us four token. And you can tell 

[05:28] of A. So there we are. We can put them all into 

[05:32] going to resolve the C issue, which is by playing 

[05:39] got a couple down here. I've made these a little 

[05:43] token copy in of B because of C. But look at this. 

[05:50] happening. And each one of them, well, the first 

[05:56] one coming in. Okay, so now we got two of those. 

[06:00] in, so it doubles those. And now we've got four 

[06:05] and doubles them. Then we get eight. And well, 

[06:10] times. So we get two to the power of five token 

[06:19] We've just put in 32 newbies. And every single 

[06:24] put two token copies of A in." So, I need to 

[06:29] what's over here? Already five A's. And they're 

[06:35] A's I did to the incoming 1B. Now, a single 

[06:41] If we have two A's coming in, it's going to 

[06:49] So, here we have this is 64 A's, which 

[06:59] no. Because if I put these in, we now have a total 

[07:08] We've done that one. We've done one of our 32 Bs. 

[07:20] make two new A's and they're going to be seen by 

[07:29] get doubled 69 times. Wow. We're about we're going 

[07:42] So, I have put these um we're now running 64 to 

[07:50] copies of A plus the 69 that were already here. 

[07:56] worked it out. Is that many? Look at that. It's 

[08:04] I didn't photocopy them all cuz if we wanted 

[08:09] if we wanted that many card A's at this scale, the 

[08:16] one entire shipping container with just paper. In 

[08:24] It would fill enough shipping containers to 

[08:31] that's a lot of paper. We'll talk more about 

[08:35] complete this journey, we're going to keep going 

[08:41] we get a number of additional A's equal to 2 to 

[08:47] So our sequence is each next term in the sequence 

[08:54] previous term plus one. And we should do that 

[09:02] up. And so the sequence goes five 69 that a lot 

[09:13] idea. Now to deal with the elephantized number in 

[09:20] And a lot of people when I said a big number 

[09:24] 52 factorial because if you take a deck of 52 

[09:30] factorial possible arrangements of this deck. But 

[09:36] number. We could write them down. I mean, I have 

[09:43] factorial. But the next step up of this, could you 

[09:49] binary it'll have that many digits because that's 

[09:57] we just divide it by it's about a third going from 

[10:03] many digits in base 10 the next one up and there's 

[10:09] absolutely not the number of atoms in the knowing 

[10:18] I've made that number up. That's 81 random digits. 

[10:25] The exact number it happens to be right now will 

[10:32] there aren't enough atoms in the universe, one 

[10:38] quickly exceeds a power bigger than the number of 

[10:45] is just nuts. In fact, if you put this whole 

[10:50] that crashes real fast. We put it into Python, 

[10:56] called hypercal. And if you do continue the number 

[11:01] this, a power tower that's 30 high. So, what we 

[11:08] you work your way down. At the top, we have 10 ^ 

[11:13] out. There's a lot. um if we could even work them 

[11:19] each layer as you go down. There are 30 of these. 

[11:25] digits as the value of the one above. And it's 

[11:34] write this in. Like this is just an insanely 

[11:43] what's amazing about playing this in Magic the 

[11:49] an exact number of Astral Dragons. And I reckon 

[11:55] game. And you can argue it's not infinitely large. 

[12:03] Now, this is a lot smaller than Graham's number. 

[12:12] towers or power towers although it was just 

[12:17] below which the value to the problem must exist. 

[12:22] some definition of vanishing and smaller, it's an 

[12:28] in that regard, this could arguably be the biggest 

[12:36] this game. It just so happens that it's so big, 

[12:43] You remember rule 107.2. If you can't calculate a 

[12:52] number. It exists. It's it's exists as much as 

[12:59] it's about as big as seven. But as humans, we 

[13:05] the shenanigans in an actual game, and there's 

[13:10] all. Like some of them are a little obscure, but 

[13:15] somehow contrived to play this in a game, depends 

[13:23] this. If they insist you need to be able to 

[13:29] proving the integer exists, you've now got zero 

[13:37] of dragons. Now, if you've enjoyed following 

[13:43] you might be the perfect person for what the 

[13:49] for us. Because speaking of shuffling things, 

[13:55] puzzle which is going to be explained by exploded 

[14:02] they are a research-driven trading firm where 

[14:07] believe that deep learning is the future of 

[14:14] machine learning team who work on neural network 

[14:21] They also have to build the infrastructure 

[14:27] that research. If you're at all interested in this 

[14:32] machine learning team have put together a neural 

[14:37] 96 layers and then they shuffled them and you 

[14:43] forget 52 factorial. To my naive understanding, 

[14:50] mean, I had a look at it. I couldn't solve this. 

[14:55] If you do think you've solved it, please send 

[15:00] see how many viewers of Standup Math videos can 

[15:07] do the puzzle. You don't have to care at all about 

[15:12] Jane Street and the work they do with machine 

[15:17] like a QR code somewhere on the screen. You can 

[15:23] That's the video. Thank you so much for watching. 

[15:27] Tabitha Grove who designed these phenomenal cards. 

[15:32] put some extra content up on there about how 

[15:38] And uh big thanks to Matthew Franklin who is the 

[15:45] thing in Magic the Gathering. And if you know 

[15:51] gathering related or otherwise, please do let 

[15:58] original Reddit post and whatnot um below. 

[16:04] you're wondering why the table's shaking slightly, 

[16:09] over here. Over here, and around. You got to say